Mixing of Random Substitutions
This dissertation investigates mixing properties of compatible random substitutions on two letters. The characterization of the mixing properties of this class of substitu- tions relies on the second eigenvalue of the associated substitution matrix. We present necessary and sufficient conditions for...
Saved in:
| Main Author: | |
|---|---|
| Format: | text |
| Published: |
Archīum Ateneo
2019
|
| Subjects: | |
| Online Access: | https://archium.ateneo.edu/theses-dissertations/449 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Ateneo De Manila University |
| Summary: | This dissertation investigates mixing properties of compatible random substitutions on two letters. The characterization of the mixing properties of this class of substitu- tions relies on the second eigenvalue of the associated substitution matrix. We present necessary and sufficient conditions for non-Pisot compatible random substitutions de- fined on two letters to be topologically mixing. This generalizes previous results on deterministic substitutions. As an intermediate result, we provide a total classification of two-letter primitive periodic substitutions. Another notion of mixing called semi- mixing is introduced which is shown to be satisfied by compatible Pisot random sub- stitutions arising from variants of the Fibonacci substitution, whose mixing properties have not been fully established. |
|---|